Question

Find the distance between
(
1
,
0
)
(1,0) and
(
9
,
15
)
(9,15).
Use the distance formula or the Pythagorean Theorem.

Answer 1

To find the distance between the points \((1, 0)\) and \((9, 15)\), we can use the distance formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Here, \((x_1, y_1) = (1, 0)\) and \((x_2, y_2) = (9, 15)\). Plugging in these values:

\[
d = \sqrt{(9 - 1)^2 + (15 - 0)^2}
\]

Calculating the differences:

\[
d = \sqrt{(8)^2 + (15)^2}
\]

Calculating the squares:

\[
d = \sqrt{64 + 225}
\]

Adding the results:

\[
d = \sqrt{289}
\]

Taking the square root:

\[
d = 17
\]

Thus, the distance between the points \((1, 0)\) and \((9, 15)\) is \(\boxed{17}\).